1. Field of the Invention
The invention is related generally to the use of resistivity measurements for evaluation of earth formations having cross-bedding.
2. Background of the Art
Electromagnetic induction and wave propagation logging tools are commonly used for determination of electrical properties of formations surrounding a borehole. These logging tools give measurements of apparent resistivity (or conductivity) of the formation that when properly interpreted are diagnostic of the petrophysical properties of the formation and the fluids therein.
The physical principles of electromagnetic induction well logging are described, for example, in, H. G. Doll, Introduction to Induction Logging and Application to Logging of Wells Drilled with Oil Based Mud, Journal of Petroleum Technology, vol. 1, p. 148, Society of Petroleum Engineers, Richardson Tex. (1949). Many improvements and modifications to electromagnetic induction resistivity instruments have been devised since publication of the Doll reference, supra. Examples of such modifications and improvements can be found, for example, in U.S. Pat. No. 4,837,517; U.S. Pat. No. 5,157,605 issued to Chandler et al, and U.S. Pat. No. 5,452,761 issued to Beard et al.
A limitation to the electromagnetic induction resistivity well logging instruments known in the art is that they typically include transmitter coils and receiver coils wound so that the magnetic moments of these coils are substantially parallel only to the axis of the instrument. Eddy currents are induced in the earth formations from the magnetic field generated by the transmitter coil, and in the induction instruments known in the art these eddy currents tend to flow in ground loops which are substantially perpendicular to the axis of the instrument. Voltages are then induced in the receiver coils related to the magnitude of the eddy currents. Certain earth formations, however, consist of thin layers of electrically conductive materials interleaved with thin layers of substantially non-conductive material. The response of the typical electromagnetic induction resistivity well logging instrument will be largely dependent on the conductivity of the conductive layers when the layers are substantially parallel to the flow path of the eddy currents. The substantially non-conductive layers will contribute only a small amount to the overall response of the instrument and therefore their presence will typically be masked by the presence of the conductive layers. The non-conductive layers, however, are the ones which are typically hydrocarbon-bearing and are of the most interest to the instrument user. Some earth formations which might be of commercial interest therefore may be overlooked by interpreting a well log made using the electromagnetic induction resistivity well logging instruments known in the art.
U.S. Pat. No. 5,999,883 issued to Gupta et al, (the “Gupta patent”), the contents of which are fully incorporated here by reference, discloses a method for determination of the horizontal and vertical conductivity of anisotropic earth formations. Electromagnetic induction signals induced by induction transmitters oriented along three mutually orthogonal axes are measured. One of the mutually orthogonal axes is substantially parallel to a logging instrument axis. The electromagnetic induction signals are measured using first receivers each having a magnetic moment parallel to one of the orthogonal axes and using second receivers each having a magnetic moment perpendicular to a one of the orthogonal axes which is also perpendicular to the instrument axis. A relative angle of rotation of the perpendicular one of the orthogonal axes is calculated from the receiver signals measured perpendicular to the instrument axis. An intermediate measurement tensor is calculated by rotating magnitudes of the receiver signals through a negative of the angle of rotation. A relative angle of inclination of one of the orthogonal axes which is parallel to the axis of the instrument is calculated, from the rotated magnitudes, with respect to a direction of the vertical conductivity. The rotated magnitudes are rotated through a negative of the angle of inclination. Horizontal conductivity is calculated from the magnitudes of the receiver signals after the second step of rotation. An anisotropy parameter is calculated from the receiver signal magnitudes after the second step of rotation. Vertical conductivity is calculated from the horizontal conductivity and the anisotropy parameter.
U.S. Pat. No. 6,466,872 to Kriegshauser et al. having the same assignee as the present application and the contents of which are fully incorporated herein by reference discloses use of a multi-component logging tool for determination of anisotropic resistivity parameters of a laminated reservoir. As would be known to those versed in the art, such a laminated reservoir that has layers of different resistivities exhibits transverse isotropy even if the layers themselves are isotropic. Such a multicomponent logging tool has azimuthal sensitivity. Kriegshauser discloses a method of analyzing data from a multicomponent logging tool to determine water saturations of the sand and shale fractions of the reservoir. The model used in Kriegshauser assumes that the anisotropy axis is normal to the bedding plane. Similar models have been assumed in, for example, in U.S. Pat. No. 6,618,676 to Kriegshauser et al., and in U.S. Pat. No. 6,643,589 to Zhang et al.
Certain types of hydrocarbon reservoirs include cross-bedding wherein within geologic markers (or beds) there is additional fine bedding (cross-bedding) with a different dip than the main bedding. Cross bedding typically occur in three major environments: (1) aeolian, (2) subaqueous delta, and (3) river channels. Due to variations in grain size, cementation, water saturation and other factors, cross-bedding usually displays resistivity anisotropy (Kennedy and Herrick, 2003). On a fine scale, the resistivity perpendicular to the cross-bedding planes is in general higher than that parallel to the cross-bedding plane. Accurate reservoir evaluation and description must consider the resistivity dependence with direction.
However, little has been understood about multicomponent induction responses in cross-bedded formations. Anderson et al. (1998) studied cross-bedding effects on coaxial-coil arrays but gave no results for multicomponent arrays. Difficulties arise in simulating induction response to a cross-bedded formation because, in the presence of a borehole, the problem must be dealt with as a general 3-D problem. The solution of the EM field quantities in Anderson takes the form of a triple Fourier integral. Anderson shows modeling results but provides little insight on the inverse problem of interpreting measured results even for coaxial arrays. It is desirable to reduce the complexity of the problem for numerical simulation and data interpretation. The present invention addresses this problem.